(1) ∵直三棱柱ABC-A1B1C1,∴A1B1//AB,CC1⊥面ABC.
∵BF⊥A1B1,∴BF⊥AB.
∵正方形AA1B1B,∴AB⊥BB1,AB=BB1=2.
∵BF∩BB1=B,∴AB⊥面BB1C1C,∴AB⊥BC.
在Rt△ABC中,∵E为AC中点,AB=BC=2,
∴==·AB·BC=1.
∵F是CC1中点,∴CF=········CC1=BB1=1
∴=·CF=·1·1=.
(2)连A1E,B1E,A1F,则A1E==,A1F==3,
EF=AC1==
∴A1E2+EF2=A1F2,∴A1E⊥EF.
由(1)在Rt△ABC中,E是AC中点,∴BE⊥AC.
∵面AA1C1C⊥面ABC,面AA1C1C∩面ABC=AC,∴BE⊥面AA1C1C
∴BE⊥A1E
∵EF∩BE=E,∴A1E⊥面BEF,∴A1E⊥BF
∵BF⊥A1B1,A1B1∩A1E=A1,∴BF⊥面A1EB1
∵DE⊂面A1EB1,∴BF⊥DE.